High-gain and high-speed wavefront shaping through scattering media

High-gain and high-speed wavefront shaping through scattering

media

Zhongtao Cheng

Chengmingyue Li

Anjul Khadria

Yide Zhang

Lihong V. Wang

Caltech Optical Imaging Laboratory, Andrew and Peggy Cherng Department of Medical

Engineering, Department of Electrical Engineering, California Institute of Technology, Pasadena,

California 91125, USA

Abstract

Wavefront shaping (WFS) is emerging as a promising tool for controlling and focusing light

in complex scattering media. The shaping system’s speed, the energy gain of the corrected

wavefronts, and the control degrees of freedom (DOF) are the most important metrics for WFS,

especially for highly scattering and dynamic samples. Despite recent advances, current methods

suffer from trade-offs that limit satisfactory performance to only one or two of these metrics.

Here, we report a WFS technique that simultaneously achieves high speed, high energy gain, and

high control DOF. By combining photorefractive crystal-based analog optical phase conjugation

(AOPC) and stimulated emission light amplification, our technique achieves an energy gain

approaching unity, more than three orders of magnitude larger than conventional AOPC. The

response time of ~10

s with about 10

control modes corresponds to an average mode time of

about 0.01 ns/mode, which is more than 50 times lower than some of the fastest WFS systems

to date. We anticipate that this technique will be instrumental in overcoming the optical diffusion

limit in photonics and translate WFS techniques to real-world applications.

Corresponding author:

LVW@caltech.edu.

Author Contributions

Z.C. and L.V.W. designed the study. Z.C. built the experimental system and performed the experiments. C.L. explored the

amplification of scattered light at the early stage of the project. A.K. and Y.Z. prepared the living animal samples and participated in

the

in vivo

experiments. L.V.W supervised the project. All the authors wrote and revised the manuscript.

Competing Interests

L.W. has a financial interest in Microphotoacoustics, Inc., CalPACT, LLC, and Union Photoacoustic Technologies, Ltd., which,

however, did not support this work. The other authors declare no conflicts of interest.

Supplementary information

The online version contains supplementary material available at https://doi.org/xxx.

Code availability

The codes used in this study are available from the corresponding author upon reasonable request.

HHS Public Access

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Published in final edited form as:

Nat Photonics

. 2023 April ; 17(4): 299–305. doi:10.1038/s41566-022-01142-4.

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Introduction

In optically complex scattering media such as biological tissues, multimode fibers, white

paper, clouds, and fog, nanoscale refractive index inhomogeneities cause optical scattering

that scrambles the wavefront of incident light. Such scattering has been a major obstacle

to efficient light delivery and focusing, hindering optical imaging, manipulation, therapy,

and stimulation beyond the optical diffusion limit. The emerging technology of wavefront

shaping (WFS) shows promise for focusing light deeply through or into complex scattering

media. By tailoring the optical wavefront incident on a scattering medium, WFS manipulates

the interference of multiply scattered light to refocus it

. To be a general tool for scattering

suppression, an ideal WFS method would have high system speed, high energy gains of the

corrected wavefronts, and high control degrees of freedom (DOF) simultaneously. To meet

the speed requirement, WFS operations must be completed within the speckle correlation

time, which physiological motion in living biological tissues typically limits to 1 ms or less.

The energy gain is defined as the ratio of the energy of the corrected wavefront to that of the

detected scattered wavefront, and it is related to the efficiency of the wavefront modulation

system

. A high energy gain ensures that the generated light focus has as much energy

as possible to facilitate applications. Generally, an energy gain approaching or exceeding

unity is highly desired. The control DOF of a WFS system determines the fineness of the

wavefront modulation, thus determining the fidelity of optical focusing, which is particularly

important for WFS in thick and highly scattering media.

To date, WFS technologies can be mainly divided into three categories: feedback-based

WFS

–

, transmission matrix inversion

–

, and optical phase conjugation (OPC)/time

reversal

–

. Feedback-based WFS and transmission matrix inversion require thousands of

measurements and wavefront updates to find a satisfactory modulation wavefront, resulting

in a long runtime that scales linearly with the number of DOF; typical runtimes are on the

level of a few seconds for methods using digital micro-mirror devices (DMDs) or more

for methods based on liquid crystal spatial light modulators (LC-SLMs). Recently, WFS

in complex media with 2.4 ms latency was demonstrated by measuring the transmission

matrix using a 1D micro-electro-mechanical system (MEMS) based phase modulator and

a fast avalanche photodiode (APD)

. However, this method works well only for WFS

in thin scattering media because of the low control DOF of the 1D MEMS. In contrast,

OPC generates the optimal incident wavefront essentially instantaneously by recording the

optical field of the scattered light and then playing back a time-reversed optical field to the

scattering medium. The field recording and time reversal can be realized by the combination

of a digital camera and a spatial light modulator (SLM), termed digital OPC (DOPC)

–

or by using a photorefractive crystal (PRC)

–

, termed analog OPC (AOPC). Limited by

the frame rates of 2D cameras, the update rates of SLMs, and data processing speeds, most

DOPC systems take more than tens of milliseconds to complete optical focusing. Recently,

a DOPC system latency of about ~1 ms was reported for a frequency-encoded wavefront

measurement approach using a single-pixel detector

. However, the achievable control DOF

(~1000) was still the biggest limitation, which is determined by the achievable independent

frequency components. AOPC can complete the field recording and time reversal within

several milliseconds to several seconds, depending on the material properties of the PRC

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employed and the illumination intensity. Different from a digital SLM with discrete pixels at

the size of several microns, a PRC can be considered as an analog SLM that has continuous

modulation units (typical spatial resolution of 5000 mm

−1

– 10000 mm

−1

)

. Therefore,

the accommodable control DOF of AOPC is much higher than that of DOPC, which means

that AOPC has the potential to realize high-fidelity optical focusing even through highly

scattering samples. However, the largest disadvantage of AOPC is its low conjugation

reflectivity, due to the weak nonlinear effect in the PRC, especially when the scattered beam

incident on the crystal is weak. Consequently, the energy gain of the time-reversed beam

is well below unity (typically 10

−3

or less). The system speeds, control DOFs and energy

gains in representative publications on WFS are compared in Supplementary Table 1 and

discussed in Supplementary Note 1.

In this article, we report a WFS modality termed high-gain high-speed WFS (HGHS-WFS)

that can simultaneously achieve high speed, high control DOF, and high energy gain.

We incorporate the concept of stimulated emission light amplification into an AOPC

realization with a fast semiconductor PRC that has a sub-millisecond response time. The

low conjugation reflectivity of the PRC is greatly compensated for by the gain from

the stimulated emission, which results in WFS energy gains approaching unity in our

experiments, more than three orders of magnitude larger than in conventional AOPC. Thanks

to the fast response of the PRC employed, as well as the amplified energy of the signal

photons, we also demonstrate a system latency as fast as ~10 microseconds with a high

control DOF of ~10

. The average mode time (i.e., the average operation time per mode) of

the technique is more than 50 times lower than that of the fastest WFS system reported to

date.

Results

Principle

The core idea of the proposed HGHS-WFS is combining the concept of stimulated emission

light amplification with an AOPC-based WFS system that employs a semiconductor PRC

with a sub-millisecond response time as the phase conjugation mirror. As schematically

illustrated in Fig. 1a, a gain module, composed of a gain medium and a pump source,

is inserted between the scattering medium and the PRC. A guidestar, which could be a

collimated laser beam or other physical or virtual light source, transmits a probe beam

through the scattering medium. A portion of the probe photons scattered through the

medium are collected and directed via a collection lens into the gain module, where

the weak scattered photons are amplified by stimulated emission light amplification. The

original and amplified probe photons are subsequently directed to the PRC and interfere

with a reference beam. Because of the photorefractive effect, information about the optical

field incident on the PRC is encoded into a volume hologram inside the PRC. In stimulated

emission, the stimulated light wave will be coherent (in phase) with the incoming wave (Fig.

1b). Therefore, the original photons and the amplified photons will have the same wavefront.

In this way, we can increase the energy of the scattered field greatly with minimal change to

its wavefront, which is significant for the subsequent time reversal. The recorded hologram

inside the PRC is read out by a conjugated reference beam, resulting in a diffracted field

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that has a conjugated phase with the incident field on the PRC (Fig. 1c). The diffracted

field retraces its trajectory through the gain module and gains energy. Similarly, since the

light amplification does not affect the wavefront of the diffracted field, the conjugation

characteristic of the amplified diffracted field is preserved. After propagating through the

scattering medium, the amplified diffracted field converges to the guidestar position as

a time-reversed wave. During all these processes, stimulated emission light amplification

plays an important role to provide gain to the scattered photons incident on the PRC

and the conjugated photons reflected off the PRC, which greatly compensates for the low

conjugation reflectivity of the PRC. Figure 1d, showing focusing through a highly scattering

optical diffuser, presents an example result of the original time-reversed focus without the

gain module, along with the result of the proposed approach.

As a proof-of-concept demonstration, we built the experimental system shown in Fig. 2

and detailed in Methods. Briefly, a near-infrared laser (1064 nm) is split into three beams

that respectively act as the probe beam, the reference beam, and the conjugated reference

beam. We employed two gain modules located in series in the path of the probe beam to

provide sufficient gain to the system. Each gain module integrates an Nd:YAG rod as the

gain medium and several laser diode arrays at 808 nm as pump sources. The pump sources

are placed around the gain medium in a side-pump mode to produce a uniform pumping

volume inside the gain medium. In our configuration, the energy of the incident light can

be increased by ~50 times after passing through each gain module (Supplementary Note 2).

The PRC here is a GaAs semiconductor, which has a response time of less than 1 ms

. In

the proof-of-concept experiments, the guidestar can be considered as the incident collimated

laser beam. Therefore, the amplified time-reversed field becomes a plane wave without

scattering after propagating through the scattering medium. To validate the time-reversal

performance, a beam splitter is inserted in front of the scattering medium to divert a copy of

the time-reversed light to a camera.

Although it is straightforward to realize time reversal via a separate hologram writing

and reading mode, here we adopt a slightly different approach: the probe beam and the

reference beam are kept on when the conjugated reference beam is reading the hologram.

Such a configuration is essentially a four-wave mixing mode

. The advantages of such

a time-reversal mode are twofold: first, the OPC reflectivity from the four-wave mixing

mode is much higher than that from the separate hologram writing and reading mode for the

GaAs PRC, as experimentally demonstrated in Supplementary Note 3. Second, eliminating

separate hologram writing and reading saves time, thus promoting the system speed. We

note that for some PRCs that have slow response speeds, lengthy writing is required to

generate a strong hologram inside the crystal. In this case, the separate hologram writing

and reading mode may be a better choice. Of course, the proposed method can be directly

applied to both time-reversal modes.

High-gain wavefront shaping through scattering media

We first demonstrate the HGHS-WFS using an optical diffuser with a diffusion angle

of ~10° (DG-120, Thorlabs) as the scattering medium. In this experiment, the power of

the scattered probe beam collected on the PRC is ~1 mW. Figure 3a shows the original

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time-reversed focus without gain, and Fig. 3b shows the cross-section along the central row

of the focus image. In contrast, Figs. 3c–3f show four typical images of the time-reversed

foci through the scattering medium at 65%, 76%, 88%, and 100% pump energy of the gain

modules we used. Note that, when capturing these four images, we placed an ND filter

providing ~1600 times attenuation in front of the camera to avoid the damage of the camera

because of the powerful intensity in the time-reversed light. For a good comparison to the

results without gain, the attenuation-corrected profiles of the central cross-sections of Figs.

3c–3f are presented in Fig. 3g. As can be seen, the peak intensity of the time-reversed

focus increases to 1.024 × 10 from the original 19 when the gain modules work at their

maximum pump powers, an increase factor of ~5390. The energy gain of the wavefront

shaping system, which is defined as the ratio of the energy in the time-reversed light to that

of the collected scattered light on the PRC, is only (1.31 ± 0.04) × 10

−4

for the original

time reversal without gain. However, our HGHS-WFS here increases the energy gain to

1.05 ± 0.02, nearly four orders of magnitude better (Supplementary Note 4). The energy

gains and the contrast-to-noise ratios (CNRs) of the time-reversed foci in Figs. 3c–3f are

presented in Fig. 3h. The CNR is defined as the ratio between the peak intensity of the

time-reversed signal above the mean of the background and the standard deviation of the

background

. Different from digital WFS where the background around the optical focus

appears as speckle patterns, in the HGHS-WFS, the background around the focus originates

from the optical noise of the gain medium, which is optically incoherent and has a uniform

intensity distribution. The CNR is a good gauge of the visibility of the focus pattern in our

case, because it evaluates both the peak intensity of the signal and the fluctuation of its

background (rather than the background DC value)

. For more illustrations about the CNR

and the peak-to-background ratio (PBR) used in digital WFS, see Supplementary Note 5.

From Fig. 3h, the energy gain of the time-reversed focus increases with the increasing pump

power of the gain modules, which is consistent with the results in Fig. 3g. We find that

the fluctuation of the background from the gain medium increases faster at a higher pump

power. Therefore, an excessively high pump power may degrade the CNR, as can be seen

in Fig. 3h. To augment the energy gain and the CNR simultaneously, it is better to raise

the phase conjugation reflectivity of the PRC (see Discussion section) while increasing the

pump power.

To demonstrate the ability of the HGHS-WFS to focus through thicker scattering samples,

we also performed experiments using different numbers of stacked optical diffusers and

chicken breast tissue slices as samples. The results are presented in Supplementary Note 6.

High-speed wavefront shaping through dynamic scattering media

To demonstrate the practical system latency of the HGHS-WFS, we mounted a 4 mm

thick piece of chicken tissue on a motorized translation stage to produce a dynamic sample

with a controllable speckle correlation time. Figure 4a shows several examples of the

speckle correlation coefficient as a function of time when the sample was moved at different

speeds (see Methods). The relationship between the speckle correlation time and the sample

movement speed is shown in Fig. 4b, where the data is fitted to a theoretical model

[

]

[

μm

[

mm s

−1

], in which

= 5.37

μm

is the fitted parameter from the experimental

data. The value

of at different speeds can be estimated from the fitted theoretical model,

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especially when the movement of the sample is so fast that the frame rate of the camera

limits the direct measurement of

. Figure 4c shows the time-reversed foci of the HGHS-

WFS for four cases: when the tissue was static (

> 1

), when it was moved at

= 300

−1

(

= 17.9 ),

= 400

mm s

−1

(

= 13.4

μs

), and = 500

mm s

−1

(

= 10.7

μs

). The

peak intensities of the time-reversed foci obtained for the sample with different correlation

times are shown in Fig. 4d. Our experiments here demonstrate that the performance of our

HGHS-WFS does not obviously vary when the sample correlation time is larger than ~15

μs

With faster speckle decorrelation, the intensity of the time-reversed focus starts to decrease,

but we can still realize time reversal successfully, even when

= 10.7

μs

, as shown in Fig.

4c.

In vivo

optical focusing through a living-mouse ear

As a final demonstration, we applied HGHS-WFS for

in vivo

optical focusing through

an area of a living mouse’s ear with many blood vessels, where strong optical scattering,

absorption, and fast speckle decorrelation co-exist. The scattering and absorption of the

blood and other fluid in the living tissue meant that only about 1% of the incident optical

power on the mouse ear could be collected to the PRC for time reversal. The speckle

correlation time of the mouse ear was measured to be about 2 ms (see Methods), as shown

in Fig. 5a. Since the collected scattered light on the PRC was quite weak in this case, no

time-reversed optical focus through the mouse ear could be observed for the conventional

AOPC without gain (Fig. 5b). In contrast, as Fig. 5c shows, a bright optical focus was

achieved with HGHS-WFS. The energy gain of the time-reversed focus is estimated to be

0.3 ± 0.01.

Discussion

We have presented an analog time reversal modality that enables WFS in scattering media

with an energy gain approaching unity, more than three orders of magnitude larger than

conventional AOPC, and at the same time with a nearly 10

μs

response time. Also,

this WFS modality maintains the intrinsically advantageous high control DOF found in

conventional AOPC. For example, the speckle size on the PRC in the 4 mm-thick chicken

tissue experiment was measured to be about 3.9

μm

; therefore, the practical number of the

speckle modes controlled by the PRC was estimated to be (

)

= (4 × 10

/3.9)

≈

1.05 ×

, where

= 4 is the effective size of the PRC and

is the speckle size on the PRC. Thus,

the average mode time is about 0.01

mode

, which is more than 50 times lower than that in

the fastest WFS system reported to date (0.6

mode

)

Here, we discuss the energy gain of the phase conjugation in HGHS-WFS, which is open for

further improvement. In Supplementary Note 7, we show that it is the low phase conjugation

reflectivity of the PRC that limits the energy gain of the time-reversed signal in our current

configuration, which is mainly due to the low optical powers of the reference and conjugated

reference beams available. Greater illumination powers on the PRC tend to produce a larger

phase conjugation reflectivity, thus a larger energy gain. For example, if the powers of the

reference and conjugated reference beams can both be increased to 1000 mW (10 times

increase with respect to the current powers), the energy gain could be improved by a factor

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of ~35. Moreover, the phase conjugation reflectivity of the PRC can be largely augmented

by applying an AC electric field to the crystal to enhance the space-charge field within the

crystal

. For example, a 10 kV/cm electric field can improve the phase conjugation

reflectivity by one order of magnitude relative to that without an external electric field. In

addition, a higher energy gain could be obtained with higher pump powers for the gain

modules. See Supplementary Note 7 for more detailed discussions. We also note that the

sample should be properly tilted with respect to the optical axis of the gain crystal, which

helps prevent stray light reflected by the sample from going back into the gain crystal and

avoid possible parasitic oscillation largely, especially when the energy gain is much higher

than unity.

Although increasing the illumination powers and applying an external high voltage to the

PRC are helpful to improve the intrinsic phase conjugation reflectivity of the PRC, the

maximum phase conjugation reflectivity that can be achieved in this way is only ~10

−3

as calculated in Supplementary Note 7, which is determined by the material properties of

the PRC. This result illustrates theoretically why the energy gain in conventional wavefront

shaping based on PRCs is generally well below unity, as mentioned in the Introduction

section. The stimulated emission light amplification in our HGHS-WFS provides a practical

solution for pushing the energy gain of AOPC close to unity or more. The ultrahigh system

speed of the HGHS-WFS benefits from the intrinsic fast response of the GaAs crystal, the

enhanced signal intensity on the PRC due to the energy amplification of the gain modules,

and the four-wave mixing mode for time reversal (Supplementary Notes 8 and 9). In some

applications where such a fast response is not required, we can also choose a slower but

more efficient PRC as an alternative to the GaAs used here.

The proposed HGHS-WFS is a general time reversal system that can work independently

for focusing through scattering media, as demonstrated here. It can also work with an

internal guidestar, such as focused ultrasound or nanoparticles that generate a nonlinear

second

‑

harmonic signal, for focusing into scattering media

. When working with

an ultrasonic guidestar, the focused ultrasound acts as a virtual light source that emits

frequency-shifted photons due to acousto-optic modulation. The system selectively time-

reverses the frequency-shifted photons and generates an optical focus at the position of the

ultrasonic focus. Because the modulation efficiency of an ultrasonic guidestar is generally

below 1%, the energy gain of the system should be improved by more than two orders to

compensate for the signal loss due to the ultrasound modulation. As analyzed above, by

simultaneously enhancing the illumination powers and applying an external electric field on

the PRC, it is quite feasible to provide a two-order improvement on the energy gain of the

HGHS-WFS. Accordingly, the HGHS-WFS could be extended to operation with ultrasonic

guidestars.

Although we only demonstrated the HGHS-WFS at 1064 nm, the concept can be adapted to

other laser wavelengths by employing corresponding gain media (see Supplementary Note

10 for detailed discussion).

Despite the great advantages of the HGHS-WFS, one disadvantage is that the amplified

spontaneous emission (ASE) of the gain modules introduces a uniform background to the

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time-reversed optical focus. In our system, we employed several polarizers to suppress the

ASE background to a relatively low level. Considering that the spectral bandwidth of ASE

is ~1 nm (Supplementary Note 11), while that of the signal light is less than 10

−5

the ASE background could be further suppressed through narrowband spectral filters that

have sub-nanometer bandwidths. Such narrowband spectral filters are technically available,

although highly customized designs are required

. Fortunately, the ASE background is

divergent and scattered further through the scattering medium. Therefore, the intensity of the

ASE background is generally much lower than that of the time-reversed focus. In addition,

since the ASE is incoherent, the ASE background through the scattering medium is very

even, which means that the time-reversed focus still has a good contrast-to-noise ratio.

Methods

Experimental setup.

As shown in Fig. 2, a narrowband single-mode laser (CL1064-300-S, CrystaLaser), with a

wavelength of 1064 nm and a linewidth of <10

−5

nm, was split into three beams through

two sets of half-wave plates (HWP) and polarizing beam splitters (PBS). The HWPs

and PBSs were used to flexibly adjust the optical power of each beam. The two beams,

reflected from the PBSs and expanded to ~4 mm diameters, constituted the reference and

conjugated reference beams, propagating through the photorefractive crystal (PRC) reversely

and collinearly, respectively. The powers of the reference and conjugated reference beams

are both set to ~100 mW in all the experiments. The transmitted beam through the PBSs was

the probe beam (~10 mW), which illuminated the scattering medium (SM). The HWP in the

path of the probe beam was to rotate the polarization of the probe beam to the perpendicular

direction. Part of the scattered light passing through the SM was collected into the two gain

modules (GM) by a two-inch lens. Each gain module integrated an Nd:YAG gain medium

(0.8% doping concentration, 6.35 mm diameter, and 140 mm length) and a pump source

into a metal case, with a circulating water system for cooling. The pump source comprised

several 808 nm laser diode arrays surrounding the gain medium, with a total peak pump

power of 10 kW (Astrum, LT). The pulse width and the peak power of the pump output

could be adjusted externally (Supplementary Note 12 shows the control flowchart of the

system). During the experiments, the temperature of the gain crystals was set to 24±0.1°C.

We connected the two GMs by a polarizer and a lens, which prevented half unpolarized ASE

noise out of one gain module from being amplified by the other gain module. Similarly, the

polarizer in front of the first gain medium reduced the ASE noise reaching the scattering

medium. In addition, a long-pass filter (LPF, FEL0950, Thorlabs) was used to filter the

remaining pump light below the wavelength of 950 nm. The light out of the GMs was

condensed onto the PRC, a GaAs semiconductor with an effective area of 5 mm × 5 mm

and a thickness of 7 mm. To observe the time-reversed focus through the SM directly, we

inserted a beam splitter (BS) before the SM to divert a copy of the time-reversed light to

a camera (DCC3240N, Thorlabs). It should be noted that the plane optics around the GMs

were slightly tilted to avoid possible self-oscillation of the GMs.

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Characterizing the speckle correlation time of samples.

To calibrate the relationship between the speckle correlation time and the sample movement

speed, we recorded the speckle patterns on the PRC plane at different times when the sample

was moving at a given speed and calculated the correlation coefficients between the first and

each of the subsequent frames of the recorded patterns. By fitting the speckle correlation

coefficient versus time using a Gaussian function, we determined the correlation time of

the sample at the given movement speed as the time during which the speckle correlation

coefficient dropped to 1/

To measure the speckle correlation coefficient of a moving chicken tissue specimen, we

placed a camera capturing a region of interest of 190 × 190 pixels at a frame rate of 100

Hz in the plane of the PRC to record the speckle patterns continuously when the tissue was

moving at a given speed. The speckle correlation coefficient at a given time was calculated

as the correlation between the speckle pattern captured at that time and the first speckle

pattern. Then the calculated speckle correlation coefficient as a function of time

was fitted

to a Gaussian function

Aexp

(− 2

⁄

) +

, where

A,B

and

are parameters to be

fitted. The fitted parameter

is just the correlation time of the sample. The above method

works only for the measurement of correlation times larger than tens of milliseconds, limited

by the frame rate of the camera recording the speckle patterns. To determine the speckle

correlation time of a moving tissue specimen at a sub-millisecond timescale, we fitted the

relationship between the measured speckle correlation time and the corresponding tissue

movement speed in low-speed cases, based on the fact that the speckle correlation time is

inversely proportional to the movement speed.

To measure the speckle correlation coefficient of a living mouse’s ear, we used a faster

sCMOS camera (PCO. Edge, PCO AG, Germany) to record speckle patterns at a higher

frame rate (2224 fps, 160 × 38 pixels, global shutter, and 0.20 ms exposure time), from

which

of the ear was obtained.

Configuration details for the HGHS-WFS experiments with fast-moving tissues.

In the experiments shown in Fig. 4, a piece of 4 mm thick chicken tissue sandwiched

between two glass slides was placed on a motorized translation stage (DDSM50, Thorlabs)

that had a maximum movement speed of 500

mm s

−1

and a maximum acceleration of

5000

mm s

−2

. When the motorized translation stage started to move, it sent a signal that

triggered a delay generator (DG645, Stanford Research Systems). A pre-designed time

delay, Δ

, was set in the delay generator, and its delayed output was the ultimate signal

that triggered the whole HGHS-WFS system. The delay time Δ

was the time required for

the motorized translation stage to accelerate to the given speed. In this way, we ensured

that the HGHS-WFS was performed after the desired movement speed of the tissue had

been reached. In addition, the starting position of the translation stage was also adjusted in

each speed configuration so that the probe light illuminated the same position of the sample

when the HGHS-WFS began, which could be easily determined by calculating the required

acceleration distance of the motor.

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In vivo

animal study.

For

in vivo

experiments, we used Hsd:Athymic Nude-Fox1

mice (Envigo), aged 10 to

11 months. All experimental procedures were carried out in conformity with laboratory

animal protocols approved by the Institutional Animal Care and Use Committee at the

California Institute of Technology. The mouse was continuously supplied with 1.5%

vaporized isoflurane in air to maintain stable anesthesia throughout the experiment. The

anesthetic state of the mouse was confirmed by pinching its hind paw. The anesthetized

mouse was laid on a customized flat animal platform that also provided anesthetic gas, and

the mouse ear was sandwiched between two glass slides to act as the scattering medium. The

body temperature of the mouse was maintained at 37 °C during the experiments.

Supplementary Material

Refer to Web version on PubMed Central for supplementary material.

Acknowledgements

The authors appreciate Prof. James Ballard’s close reading of the paper and Prof. Mark Cronin-Golomb’s

discussions on the photorefractive theory. This work was financially supported by US National Institutes of Health

(NIH) grants R35 CA220436 (Outstanding Investigator Award) and R01 EB028277.

Data availability

All data that support the findings of this study are available within the Article and

Supplementary Information, or available from the corresponding author upon reasonable

request.

References

1. Vellekoop IM and Mosk AP, “Focusing coherent light through opaque strongly scattering media,”

Opt. Lett. 32, 2309–2311 (2007). [PubMed: 17700768]

2. Mosk AP, Lagendijk A, Lerosey G, and Fink M, “Controlling waves in space and time for imaging

and focusing in complex media,” Nature Photonics 6, 283–292 (2012).

3. Wang YM, Judkewitz B, DiMarzio CA, and Yang C, “Deep-tissue focal fluorescence imaging with

digitally time-reversed ultrasound-encoded light,” Nature Communications 3, 928 (2012).

4. Akbulut D, Huisman TJ, van Putten EG, Vos WL, and Mosk AP, “Focusing light through random

photonic media by binary amplitude modulation,” Opt. Express 19, 4017–4029 (2011). [PubMed:

21369229]

5. Katz O, Small E, Bromberg Y, and Silberberg Y, “Focusing and compression of ultrashort pulses

through scattering media,” Nature Photonics 5, 372–377 (2011).

6. Conkey DB, Brown AN, Caravaca-Aguirre AM, and Piestun R, “Genetic algorithm optimization

for focusing through turbid media in noisy environments,” Opt. Express 20, 4840–4849 (2012).

[PubMed: 22418290]

7. Lai P, Wang L, Tay JW, and Wang LV, “Photoacoustically guided wavefront shaping for enhanced

optical focusing in scattering media,” Nature Photonics 9, 126 (2015). [PubMed: 25914725]

8. Blochet B, Bourdieu L, and Gigan S, “Focusing light through dynamical samples using fast

continuous wavefront optimization,” Opt. Lett. 42, 4994–4997 (2017). [PubMed: 29216164]

9. Frostig H, et al. , “Focusing light by wavefront shaping through disorder and nonlinearity,” Optica 4,

1073–1079 (2017).

10. Jang M, et al. , “Wavefront shaping with disorder-engineered metasurfaces,” Nature Photonics 12,

84–90 (2018). [PubMed: 29527234]

Cheng et al.

Page 10

Nat Photonics

. Author manuscript; available in PMC 2024 April 01.

Author Manuscript

11. Nixon M, et al. , “Real-time wavefront shaping through scattering media by all-optical feedback,”

Nature Photonics 7, 919–924 (2013).

12. Popoff SM, et al. , “Measuring the Transmission Matrix in Optics: An Approach to the Study and

Control of Light Propagation in Disordered Media,” Physical Review Letters 104, 100601 (2010).

[PubMed: 20366410]

13. Kim M, et al. , “Maximal energy transport through disordered media with the implementation of

transmission eigenchannels,” Nature Photonics 6, 581–585 (2012).

14. Boniface A, Mounaix M, Blochet B, Piestun R, and Gigan S, “Transmission-matrix-based point-

spread-function engineering through a complex medium,” Optica 4, 54–59 (2017).

15. Mounaix M, de Aguiar HB, and Gigan S, “Temporal recompression through a scattering medium

via a broadband transmission matrix,” Optica 4, 1289–1292 (2017).

16. Yılmaz H, Hsu CW, Yamilov A, and Cao H, “Transverse localization of transmission

eigenchannels,” Nature Photonics 13, 352–358 (2019).

17. Mounaix M, et al. , “Spatiotemporal Coherent Control of Light through a Multiple Scattering

Medium with the Multispectral Transmission Matrix,” Physical Review Letters 116, 253901

(2016). [PubMed: 27391722]

18. Conkey DB, Caravaca-Aguirre AM, and Piestun R, “High-speed scattering medium

characterization with application to focusing light through turbid media,” Opt. Express 20, 1733–

1740 (2012). [PubMed: 22274516]

19. Li S, Horsley SAR, Tyc T, Čižmár T, and Phillips DB, “Memory effect assisted imaging through

multimode optical fibres,” Nature Communications 12, 3751 (2021).

20. Cui M and Yang C, “Implementation of a digital optical phase conjugation system and its

application to study the robustness of turbidity suppression by phase conjugation,” Opt. Express

18, 3444–3455 (2010). [PubMed: 20389354]

21. Hsieh C-L, Pu Y, Grange R, and Psaltis D, “Digital phase conjugation of second harmonic

radiation emitted by nanoparticles in turbid media,” Opt. Express 18, 12283–12290 (2010).

[PubMed: 20588353]

22. Liu Y, Ma C, Shen Y, Shi J, and Wang LV, “Focusing light inside dynamic scattering media with

millisecond digital optical phase conjugation,” Optica 4, 280–288 (2017). [PubMed: 28815194]

23. Cheng Z, Yang J, and Wang LV, “Intelligently optimized digital optical phase conjugation with

particle swarm optimization,” Opt. Lett. 45, 431–434 (2020). [PubMed: 32747844]

24. Ruan H, et al. , “Deep tissue optical focusing and optogenetic modulation with time-reversed

ultrasonically encoded light,” Science Advances 3, eaao5520 (2017).

25. Ma C, Xu X, Liu Y, and Wang LV, “Time-reversed adapted-perturbation (TRAP) optical focusing

onto dynamic objects inside scattering media,” Nature Photonics 8, 931 (2014). [PubMed:

25530797]

26. Feldkhun D, Tzang O, Wagner KH, and Piestun R, “Focusing and scanning through scattering

media in microseconds,” Optica 6, 72–75 (2019).

27. Wang D, et al. , “Focusing through dynamic tissue with millisecond digital optical phase

conjugation,” Optica 2, 728–735 (2015). [PubMed: 26677458]

28. Cheng Z and Wang LV, “Focusing light into scattering media with ultrasound-induced field

perturbation,” Light: Science & Applications 10, 159 (2021).

29. Yaqoob Z, Psaltis D, Feld MS, and Yang C, “Optical phase conjugation for turbidity suppression in

biological samples,” Nature Photonics 2, 110 (2008). [PubMed: 19492016]

30. Xu X, Liu H, and Wang LV, “Time-reversed ultrasonically encoded optical focusing into scattering

media,” Nature Photonics 5, 154 (2011). [PubMed: 21532925]

31. Liu Y, et al. , “Optical focusing deep inside dynamic scattering media with near-infrared time-

reversed ultrasonically encoded (TRUE) light,” Nature Communications 6, 5904 (2015).

32. Tzang O, et al. , “Wavefront shaping in complex media with a 350 kHz modulator via a 1D-to-2D

transform,” Nature Photonics 13, 788–793 (2019).

33. Cheng Z, Yang J, and Wang LV, “Dual-polarization analog optical phase conjugation for

focusing light through scattering media,” Applied Physics Letters 114, 231104 (2019). [PubMed:

31312071]

Cheng et al.

Page 11

Nat Photonics

. Author manuscript; available in PMC 2024 April 01.

Author Manuscript

34. Wei X, et al. , “Real-time frequency-encoded spatiotemporal focusing through scattering media

using a programmable 2D ultrafine optical frequency comb,” Science Advances 6(2020).

35. Hariharan P, Basics of holography (Cambridge university press, 2002).

36. Klein MB, “Beam coupling in undoped GaAs at 1.06 μm using the photorefractive effect,” Opt.

Lett. 9, 350–352 (1984). [PubMed: 19721595]

37. Boyd RW, Nonlinear Optics (Academic Press, Inc., 2008).

38. Wang LV and Wu H, Biomedical Optics: Principles and Imaging (John Wiley & Sons, 2007).

39. Ruan H, Xu J, and Yang C, “Optical information transmission through complex scattering media

with optical-channel-based intensity streaming,” Nature Communications 12, 2411 (2021).

40. Kumar J, Albanese G, Steier WH, and Ziari M, “Enhanced two-beam mixing gain in

photorefractive GaAs using alternating electric fields,” Opt. Lett. 12, 120–122 (1987). [PubMed:

19738812]

41. Klein MB, McCahon SW, Boggess TF, and Valley GC, “High-accuracy, high-reflectivity phase

conjugation at 1.06 μm by four-wave mixing in photorefractive gallium arsenide,” J. Opt. Soc. Am.

B 5, 2467–2472 (1988).

42. Horstmeyer R, Ruan H, and Yang C, “Guidestar-assisted wavefront-shaping methods for focusing

light into biological tissue,” Nature Photonics 9, 563–571 (2015). [PubMed: 27293480]

43. Fredell M, Carver G, Chanda S, Locknar S, and Johnson R, Sub-nanometer band pass coatings for

LIDAR and astronomy, SPIE Optical Engineering + Applications (SPIE, 2015), Vol. 9612.

Cheng et al.

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Figure 1. Principle of the HGHS-WFS.

, The probe beam scattered through the scattering medium is collected and directed to a

gain module, which is composed of a gain medium and a pump source. The weak scattered

photons are amplified in the gain module by stimulated emission light amplification and

subsequently interfere with a reference beam to form a volume hologram inside the PRC.

Illustration of stimulated emission light amplification in a typical four-level gain medium,

as used in our experiments. E1–E4 denote the simplified four energy levels involved in

the stimulated emission light amplification.

, Reading the hologram inside the PRC using

a conjugated reference beam results in a weak time-reversed beam, which retraces its

trajectory through the gain module and gains energy without change to its wavefront. After

propagating through the scattering medium, the amplified time-reversed beam converges

to the guidestar position.

, An example of the original time-reversed focus without the

gain module, compared with the result of the proposed approach when focusing through a

highly scattering optical diffuser. Note that the time-reversed focus with gain is attenuated

by ~1600 times to avoid camera over-exposure.

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Figure 2. Schematic of the experimental setup.

BS, beam splitter; GM, gain module; HWP, half-wave plate; LPF, long-pass filter; P,

polarizer; PBS, polarizing beam splitter; PRC, photorefractive crystal; SM, scattering

medium. The inset shows photos of the gain modules used in the experiments.

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Figure 3. Experimental demonstrations of the HGHS-WFS at different pump powers of the gain

modules.

, Original time-reversed focus without gain.

, Cross-section profile along the central

row of the focus image in

, Four typical images of the obtained time-reversed foci

through the scattering medium at 65%, 76%, 88%, and 100% pump energy of the gain

modules we used. When capturing these four images, we placed an ND filter providing

~1600 times attenuation in front of the camera.

, Attenuation-corrected profiles of the

central cross-sections of

c-f

, Energy gains and CNRs (contrast-to-noise ratios) of the

time-reversed foci in Figs. 3c–3f (as well as the foci at other pump energies whose images

are not shown).

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Figure 4. Focusing through fast dynamic scattering samples.

, Examples showing the speckle correlation coefficient as a function of time when the

sample was moved at different speeds.

, Relationship between the speckle correlation time

and the sample movement speed. The error bars show the standard deviations of

measured

when light illuminated four different locations on the tissue.

, The time-reversed foci of the

HGHS-WFS when a 4 mm thick piece of tissue was static (

> 1 ), moved at

= 300

−1

(

= 17.9

μs

= 400

mm s

−1

(

= 13.4

μs

), and

= 500

mm s

−1

(

= 10.7

μs

Peak intensities of the time-reversed foci through the sample with different correlation times.

The error bars show the standard deviations of the peak intensities of three time-reversed

foci.

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